Suppose V is a vector space that is not necessarily finite-dimensional. Suppose S is a subset of V that is not necessarily finite. Given a linear transformation T : V → V , define the image of S under T to be the set T(S) = {wE V : 3v E S, w = T(v)} (1) Prove that if T(v) is linearly independent, then S is linearly independent. (2) Justify whether it is true that if S is linearly independent then T(v) must be linearly independent.

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